The large \(N_C\)  study of the partial-wave \(\pi \pi \)  scattering by including the crossed-channel effects gives an updated KSRF relation \(G_V=F_\pi /\sqrt{3}\)  [1]}, [2]}. Based on the revised KSRF relation, alternative high energy relations can be obtained [3]}, [4]}, [5]}
\(F_A=\sqrt{2} F_\pi ,\quad F_V=\sqrt{3} F_\pi , \quad G_V= F_\pi /\sqrt{3} \,.\) 
